Multiple-input multiple-output (MIMO) techniques have become one of the most essential parts of wireless communications systems. Indeed, IEEE 802.16e specifications include several MIMO profiles for two, three and four transmit antennas, and provide transmit diversity, spatial multiplexing (SM) or the advantages of both. However, the current IEEE 802.16e specifications lack a covering of all the interesting space-time codes (STCs) which benefit efficiently from transmit diversity exploited by forward error correction (FEC).
In the IEEE 802.16e specification, the schemes which exploit transmit diversity using STC and/or FEC are defined for two, three, and four transmit antennas. Below, we use the notation XM for denoting matrix X with M rows (rows corresponding to the total number of antennas).
For two transmit antennas a first scheme, namely, coding matrix A2, is defined as:
                              A          ⁢                                          ⁢          2                =                  [                                                                      s                  1                                                                              -                                      s                    2                    *                                                                                                                        s                  2                                                                              s                  1                  *                                                              ]                                    (        1        )            
s1, and s2 being respectively first and second symbols, and the star designating the complex conjugate.
The scheme defined by the matrix A2 is based on the Alamouti code for transmit diversity (as described in the article S. M. Alamouti, “A simple transmit diversity technique for wireless communications” IEEE Journal on selected areas in communications, vol. 16, n°. 8, pp. 1451-1458, October 1998, which is incorporated by reference.), and consists of grouping the input data symbols two by two and transmitting a pair of symbols (s1,s2) through two transmit antennas over two time slots (or transmission intervals). Here, the columns correspond to the time slots and the rows correspond to the transmit antennas. Therefore, transmission of coding matrix A2 is realized over two time slots using two transmit antennas.
A second scheme, namely, matrix B2, is based on spatial multiplexing (SM) and is described by:
                              B          ⁢                                          ⁢          2                =                  [                                                                      s                  1                                                                                                      s                  2                                                              ]                                    (        2        )            
This scheme is full rate since two symbols are transmitted over two transmit antennas in one time slot but it suffers from diversity loss.
For a higher number of antennas, the generalized forms of Alamouti code and spatial multiplexing (SM) are provided to improve the performance while keeping the detection complexity reasonable. For three transmit antennas the 2×2 STCs given above are generalized as:
                                          A            ⁢                                                  ⁢            3                    =                      [                                                                                s                    1                                                                                        -                                          s                      2                      *                                                                                        0                                                  0                                                                                                  s                    2                                                                                        s                    1                    *                                                                                        s                    3                                                                                        -                                          s                      4                      *                                                                                                                    0                                                  0                                                                      s                    4                                                                                        s                    3                    *                                                                        ]                          ,                                  ⁢                              B            ⁢                                                  ⁢            3                    =                      [                                                                                                                                                        s                          1                                                                                                                                                              s                          2                                                                                                                                                                                      s                    3                                                                        ]                                              (        3        )            
The matrix A3 benefits from transmit diversity exploited from both (Alamouti) and FEC encoder/decoder. However, SM defined with B3 benefits only from FEC encoder/decoder to exploit transmit diversity.
Similar to the three transmit antennas case, generalized schemes in IEEE 802.16e for four transmit antennas can be defined as:
                                          A            ⁢                                                  ⁢            4                    =                      [                                                                                s                    1                                                                                        -                                          s                      2                      *                                                                                        0                                                  0                                                                                                  s                    2                                                                                        s                    1                    *                                                                    0                                                  0                                                                              0                                                  0                                                                      s                    3                                                                                        -                                          s                      4                      *                                                                                                                    0                                                  0                                                                      s                    4                                                                                        s                    3                    *                                                                        ]                          ,                                  ⁢                              B            ⁢                                                  ⁢            4                    =                      [                                                                                                                                                        s                          1                                                                                                                                                              s                          2                                                                                                                                                                                                                                                              s                          3                                                                                                                                                              s                          4                                                                                                                                          ]                                              (        4        )            
Again the matrix A4 benefits from transmit diversity exploited by STC and FEC, but the matrix B4 (based on SM scheme) only benefits from transmit diversity exploited by FEC encoder/decoder. All of the schemes mentioned above can also be defined over only the frequency dimension or over both the frequency and time dimensions instead of only over the time dimension.
The patent application US 2007/0183527, which is incorporated herein by reference, provides different alternatives of STCs employing Alamouti code (that is to say involving the use of complex conjugate of the symbol to be transmitted) which have the ability to exploit more transmit diversity with the help of FEC. Their primary goal is to introduce codes which exploit the properties of FEC codes to maintain the advantages of Alamouti codes. Although this transmission scheme provides a better performance than the pure Alamouti scheme, it also suffers from the same rate loss as Alamouti.